1. Field of the Invention
This invention relates to a simulation method and a simulation program for simulating the feature profile of a material surface such as a semiconductor device.
2. Background Art
In the processing of a material surface using chemical vapor deposition and reactive ion etching, simulation of the feature profile is a necessary technique for sophisticated process control. Semiconductor manufacturing processes including fine processing require high accuracy in process controllability, and simulation also requires similar high accuracy.
Simulation of the feature profile of a material surface is typically performed by dividing the material surface in a microstructure into finite computational elements (such as points, segments, and polygons) and calculating the flux or surface growth rate at each computational element. There is a simulation method for determining the feature profile by dividing a material surface into finite computational elements, determining a local flux at each computational element, and calculating a surface growth rate for each time step based on a surface reaction model (e.g., G. Kokkoris, A. Tserepi, A. G. Boudouvis, and E. Gogolides, “Simulation of SiO2 and Si feature etching for microelectronics and microelectromechanical systems fabrication”, J. Vac. Sci. Technol. A 22, 1896 (2004)).
The feature profile evolution is performed by various techniques such as a technique based on the level set method (e.g., G. Kokkoris, A. Tserepi, A. G. Boudouvis, and E. Gogolides, “Simulation of SiO2 and Si feature etching for microelectronics and microelectromechanical systems fabrication”, J. Vac. Sci. Technol. A 22, 1896 (2004)), a technique based on the cell model (A. P. Mahorowala and H. H. Sawin, “Etching of polysilicon in inductively coupled Cl2 and HBr discharges. II. Simulation of profile evolution using cellular representation of feature composition and Monte Carlo computation of flux and surface kinetics”, J. Vac. Sci. Technol. B 20, 1064 (2002)), and a technique based on the string model. Any of these techniques is typically performed by dividing the material surface in a microstructure into finite computational elements (such as points, segments, and polygons) and determining the flux or surface growth rate at each computational element.
In the processing of a material surface, it is known that the feature profile is greatly affected by not only reactive species directly reaching the material surface from the vapor phase, but also by reactive species once brought into contact with another material and then indirectly reaching the material surface. Both experiments and simulations have shown that anomalous features called “microtrenches” are produced by ions reaching the material surface from the vapor phase and reflected thereon, as disclosed in, e.g., S. Abdollahi-Alibeik, J. P. McVittie, K. C. Saraswat, V. Sukharev, and P. Schoenborn, “Analytical modeling of silicon etch process in high density plasma”, J. Vac. Sci. Technol. A 17, 2485 (1999). In the simulation of feature profiles described in this paper, the material surface in a microstructure is divided into finite computational elements, and the amount of ions reflected from one computational element to another is calculated on the basis of a reflection probability, which is defined before calculation and depends on the emission angle. Thus, anomalous features called microtrenches are represented.
However, use of techniques for representing the material surface by dividing it into finite computational elements (such as points, segments, and polygons) may introduce profile error. In particular, in calculating an indirect effect of one computational element on another (such as reflection and resputtering), finite division of the material surface induces error, which has the problem of greatly affecting the profile accuracy of the calculated result.